Algebra teacher’s activities kit : 150 activities that support algebra in the common core math standards, grades 6-12

Abstract

CONTENTS About the Authors vii Acknowledgments ix Preface xvii SECTION 1: RATIOS AND PROPORTIONAL RELATIONSHIPS 1 Teaching Notes for the Activities of Section 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1–1: (6.RP.1) Understanding Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1–2: (6.RP.2) Unit Rates and Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1–3: (6.RP.3) Equivalent Ratios and the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . 3 1–4: (6.RP.3) Finding the Percent of a Number and Finding the Whole . . . . . . . . . . . . . 3 1–5: (7.RP.1) Finding Unit Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1–6: (7.RP.2) Graphing Proportional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1–7: (7.RP.2) Representing Proportional Relationships. . . . . . . . . . . . . . . . . . . . . . . . . 5 1–8: (7.RP.3) Solving Word Problems Involving Percents . . . . . . . . . . . . . . . . . . . . . . . . 5 Reproducibles for Section 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 SECTION 2: THE NUMBER SYSTEM AND NUMBER AND QUANTITY 19 Teaching Notes for the Activities of Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2–1: (6.NS.5) Representing Positive and Negative Numbers . . . . . . . . . . . . . . . . . . . . 20 2–2: (6.NS.6) Graphing Rational Numbers on a Number Line . . . . . . . . . . . . . . . . . . . 20 2–3: (6.NS.6) Graphing Points in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . 21 2–4: (6.NS.7) The Absolute Value and Order of Rational Numbers . . . . . . . . . . . . . . . 22 2–5: (6.NS.8) Using the Coordinate Plane to Solve Problems . . . . . . . . . . . . . . . . . . . 22 2–6: (7.NS.1) Using the Number Line to Add and Subtract Rational Numbers. . . . . . . 23 2–7: (7.NS.1) Using Properties to Add and Subtract Rational Numbers . . . . . . . . . . . 24 2–8: (7.NS.2) Multiplying and Dividing Rational Numbers . . . . . . . . . . . . . . . . . . . . . . 25 2–9: (7.NS.2) Converting Rational Numbers to Decimals. . . . . . . . . . . . . . . . . . . . . . . 26 2–10: (7.NS.3) Solving Word Problems Involving Rational Numbers . . . . . . . . . . . . . . 27 2–11: (8.NS.1) Expressing Fractions as Repeating Decimals and Repeating Decimals as Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2–12: (8.NS.2) Using Rational Approximations of Irrational Numbers . . . . . . . . . . . . . 28 2–13: (N-RN.1) Using the Properties of Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2–14: (N-RN.2) Rewriting Expressions Involving Radicals and Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2–15: (N-RN.3) Sums and Products of Rational and Irrational Numbers . . . . . . . . . . . 30 2–16: (N-Q.1) Interpreting and Using Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2–17: (N-Q.2) Defining Appropriate Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2–18: (N-Q.3) Choosing Appropriate Levels of Accuracy for Measurement . . . . . . . . . 32 2–19: (N-CN.1) Writing Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2–20: (N-CN.2) Adding, Subtracting, and Multiplying Complex Numbers . . . . . . . . . . . 34 2–21: (N-CN.7) Solving Quadratic Equations That Have Complex Solutions . . . . . . . . 34 Reproducibles for Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 SECTION 3: BASIC EXPRESSIONS, EQUATIONS, AND INEQUALITIES 60 Teaching Notes for the Activities of Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3–1: (6.EE.1) Writing and Evaluating Numerical Expressions with Whole-Number Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3–2: (6.EE.2) Writing and Reading Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . 62 3–3: (6.EE.2) Evaluating Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3–4: (6.EE.3) Applying Properties of Operations to Generate Equivalent Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3–5: (6.EE.4) Identifying Equivalent Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3–6: (6.EE.5) Identifying Solutions of Equations and Inequalities . . . . . . . . . . . . . . . . 64 3–7: (6.EE.6) Writing Expressions in Which Variables Represent Numbers . . . . . . . . . 64 3–8: (6.EE.7) Writing and Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3–9: (6.EE.8) Using Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3–10: (6.EE.9) Using Variables to Represent Two Quantities . . . . . . . . . . . . . . . . . . . . 66 3–11: (7.EE.1) Adding, Subtracting, Factoring, and Expanding Linear Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3–12: (7.EE.2) Rewriting Expressions in Different Forms . . . . . . . . . . . . . . . . . . . . . . . 67 3–13: (7.EE.3) Solving Multi-Step Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3–14: (7.EE.4) Solving Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3–15: (8.EE.1) Applying Properties of Integer Exponents . . . . . . . . . . . . . . . . . . . . . . . 69 3–16: (8.EE.2) Using Square Roots and Cube Roots . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3–17: (8.EE.3) Using Numbers Expressed in Scientific Notation . . . . . . . . . . . . . . . . . 70 3–18: (8.EE.4) Operations with Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3–19: (8.EE.5) Graphing Proportional Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3–20: (8.EE.6) Deriving the Equation y = mx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3–21: (8.EE.7) Identifying Equations That Have One Solution, No Solutions, or Infinitely Many Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3–22: (8.EE.7) Solving Equations with Variables on Both Sides . . . . . . . . . . . . . . . . . 73 3–23: (8.EE.8) Solving Systems of Linear Equations Algebraically . . . . . . . . . . . . . . . 74 3–24: (8.EE.8) Solving Systems of Equations by Graphing . . . . . . . . . . . . . . . . . . . . . 75 Reproducibles for Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 SECTION 4: POLYNOMIAL, RATIONAL, EXPONENTIAL, AND RADICAL EXPRESSIONS, EQUATIONS, AND INEQUALITIES 103 Teaching Notes for the Activities of Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4–1: (A-SSE.1) Interpreting Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4–2: (A-SSE.2) Using the Structure of an Expression to Identify Ways to Rewrite It . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4–3: (A-SSE.3) Factoring Quadratic Expressions to Reveal Zeroes . . . . . . . . . . . . . . . 105 4–4: (A-SSE.3) Completing the Square to Reveal Maximum or Minimum Values . . . . . 106 4–5: (A-SSE.4) Finding Sums of Finite Geometric Series . . . . . . . . . . . . . . . . . . . . . . .106 4–6: (A-APR.1) Adding, Subtracting, and Multiplying Polynomials . . . . . . . . . . . . . . . . .107 4–7: (A-APR.2) Applying the Remainder Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107 4–8: (A-APR.3) Using Zeroes to Construct a Rough Graph of a Polynomial Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108 4–9: (A-APR.4) Proving Polynomial Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 4–10: (A-APR.6) Rewriting Rational Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110 4–11: (A-CED.1) Writing and Solving Equations and Inequalities in One Variable . . . . .111 4–12: (A-CED.2) Writing and Graphing Equations in Two Variables . . . . . . . . . . . . . . . .111 4–13: (A-CED.3) Representing Constraints and Interpreting Solutions . . . . . . . . . . . . .112 4–14: (A-CED.4) Highlighting Quantities of Interest in Formulas . . . . . . . . . . . . . . . . . .113 4–15: (A-REI.1) Justifying Solutions to Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113 4–16: (A-REI.2) Solving Rational and Radical Equations. . . . . . . . . . . . . . . . . . . . . . . .114 4–17: (A-REI.3) Solving Multi-Step Linear Equations in One Variable . . . . . . . . . . . . . .115 4–18: (A-REI.3) Solving Multi-Step Linear Inequalities in One Variable . . . . . . . . . . . . .115 4–19: (A-REI.4) Solving a Quadratic Equation by Completing the Square . . . . . . . . . . .116 4–20: (A-REI.4) Solving Quadratic Equations in a Variety of Ways . . . . . . . . . . . . . . . .116 4–21: (A-REI.5) Solving Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117 4–22: (A-REI.6) Solving Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . .118 4–23: (A.REI.7) Solving a System of a Linear and a Quadratic Equation . . . . . . . . . . .118 4–24: (A-REI.10) Relating Graphs to the Solutions of Equations . . . . . . . . . . . . . . . . .119 4–25: (A-REI.11) Using Graphs and Tables to Find Solutions to Systems of Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .120 4–26: (A-REI.12) Solving Systems of Inequalities by Graphing . . . . . . . . . . . . . . . . . . .120 Reproducibles for Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121 SECTION 5: FUNCTIONS 155 Teaching Notes for the Activities of Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 5–1: (8.F.1) Identifying Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .156 5–2: (8.F.2) Comparing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157 5–3: (8.F.3) Determining Whether Data Lies on a Line . . . . . . . . . . . . . . . . . . . . . . . . .157 5–4: (8.F.4) Finding the Slope and Y-Intercept of a Line . . . . . . . . . . . . . . . . . . . . . . . .157 5–5: (8.F.5) Analyzing and Graphing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .158 5–6: (F-IF.1) Understanding Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 5–7: (F-IF.2) Finding the Values of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159 5–8: (F-IF.3) Defining Sequences Recursively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 5–9: (F-IF.4) Identifying Key Features of Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .160 5–10: (F-IF.5) Relating the Domain of a Function to Its Graph or Description . . . . . . . .161 5–11: (F-IF.6) Finding the Average Rate of Change over Specified Intervals . . . . . . . . .162 5–12: (F-IF.7) Graphing Linear and Quadratic Functions . . . . . . . . . . . . . . . . . . . . . . . .162 5–13: (F-IF.7) Graphing Polynomial Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 5–14: (F-IF.8) Rewriting Quadratic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164 5–15: (F-IF.9) Comparing Properties of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 5–16: (F-BF.1) Writing Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .165 5–17: (F-BF.2) Writing Arithmetic and Geometric Sequences . . . . . . . . . . . . . . . . . . . .166 5–18: (F-BF.3) Transforming a Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 5–19: (F-BF.4) Finding the Inverses of Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5–20: (F-LE.1) Proving Linear Functions Grow by Equal Differences over Equal Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5–21: (F-LE.1) Proving Exponential Functions Grow by Equal Factors over Equal Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 5–22: (F-LE.2) Constructing Linear and Exponential Functions . . . . . . . . . . . . . . . . . . 169 5–23: (F-LE.3) Observing the Behavior of Quantities That Increase Exponentially . . . . 170 5–24: (F-LE.4) Writing and Solving Exponential Equations . . . . . . . . . . . . . . . . . . . . . . 170 5–25: (F-LE.5) Interpreting Parameters in a Linear or Exponential Function . . . . . . . . . 171 5–26: (F-TF.1) Using Radian and Degree Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5–27: (F-TF.2) Using the Unit Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5–28: (F-TF.5) Modeling Periodic Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 5–29: (F-TF.8) Finding the Values of the Sine, Cosine, and Tangent Functions . . . . . . 174 Reproducibles for Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 SECTION 6: STATISTICS AND PROBABILITY 221 Teaching Notes for the Activities of Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6–1: (6.SP.1) Identifying Statistical Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6–2: (6.SP.2) Describing Data Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 6–3: (6.SP.3) Finding the Mean, Median, Mode, and Range . . . . . . . . . . . . . . . . . . . . . 223 6–4: (6.SP.4) Using Dot Plots to Display Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6–5: (6.SP.4) Constructing a Box Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 6–6: (6.SP.5) Summarizing and Describing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 6–7: (7.SP.1) Drawing Inferences from Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 6–8: (7.SP.2) Drawing Inferences about a Population Using Random Samples . . . . . . 227 6–9: (7.SP.3) Comparing Two Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 6–10: (7.SP.4) Drawing Inferences about Populations . . . . . . . . . . . . . . . . . . . . . . . . . 229 6–11: (7.SP.5) Understanding the Probability of Events . . . . . . . . . . . . . . . . . . . . . . . . 229 6–12: (7.SP.6) Probabilities and Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 6–13: (7.SP.7) Using Probability Models to Find Probabilities of Events . . . . . . . . . . . . 230 6–14: (7.SP.8) Understanding the Probability of Compound Events . . . . . . . . . . . . . . . 231 6–15: (7.SP.8) Finding Probabilities of Compound Events Using Tables, Lists, and Tree Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 6–16: (8.SP.1) Constructing and Interpreting Scatter Plots . . . . . . . . . . . . . . . . . . . . . 233 6–17: (8.SP.2) Fitting Lines to Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 6–18: (8.SP.3) Using Equations of Linear Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 6–19: (8.SP.4) Constructing and Interpreting Two-Way Tables . . . . . . . . . . . . . . . . . . . . 235 6–20: (S-ID.1) Representing Data with Plots on the Real Number Line . . . . . . . . . . . . 236 6–21: (S-ID.2) Comparing Two Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 6–22: (S-ID.3) Interpreting Differences in Shape, Center, and Spread of Data Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 6–23: (S-ID.4) Recognizing Characteristics of Normal Distributions . . . . . . . . . . . . . . . 238 6–24: (S-ID.5) Summarizing Categorical Data in Two-Way Frequency Tables . . . . . . . . 238 6–25: (S-ID.6) Finding the Equation of the Line of Best Fit . . . . . . . . . . . . . . . . . . . . . 239 6–26: (S-ID.6) Using Linear and Quadratic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 6–27: (S-ID.7) Interpreting the Slope and Y-Intercept of a Linear Model . . . . . . . . . . . 241 6–28: (S-ID.8) Computing and Interpreting the Correlation Coefficient . . . . . . . . . . . . 241 6–29: (S-ID.9) Distinguishing between Correlation and Causation . . . . . . . . . . . . . . . .242 6–30: (S-IC.1) Understanding the Terminology of Statistical Experiments . . . . . . . . . .242 6–31: (S-IC.2) Evaluating Probability Models through Simulations . . . . . . . . . . . . . . . .243 6–32: (S-IC.3) Recognizing Surveys, Experiments, and Observational Studies . . . . . .244 6–33: (S-IC.4) Using Simulations with Random Sampling . . . . . . . . . . . . . . . . . . . . . .244 6–34: (S-IC.5) Comparing Two Treatments Using Simulations . . . . . . . . . . . . . . . . . . .245 6–35: (S-IC.6) Evaluating Data in Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .246 6–36: (S-CP.1) Describing Events as Subsets of a Sample Space . . . . . . . . . . . . . . . .246 6–37: (S-CP.2) Identifying Independent Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .247 6–38: (S-CP.3) Interpreting Conditional Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . .247 6–39: (S-CP.4) Understanding Two-Way Frequency Tables . . . . . . . . . . . . . . . . . . . . . . .248 6–40: (S-CP.5) Exploring Concepts of Conditional Probability . . . . . . . . . . . . . . . . . . . .249 6–41: (S-CP.6) Finding Conditional Probabilities as a Fraction of Outcomes . . . . . . . . .249 6–42: (S-CP.7) Applying the Addition Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250 Reproducibles for Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .250 INDEX 305